1. Technical Field
The present invention relates to computer-implemented pharmacokinetic simulation models and drug design.
2. Background
A. Pharmacokinetic Modeling
Pharmacodynamics refers to the study of fundamental or molecular interactions between drug and body constituents, which through a subsequent series of events results in a pharmacological response. For most drugs the magnitude of a pharmacological effect depends on time-dependent concentration of drug at the site of action (e.g., target receptor-ligand/drug interaction). Factors that influence rates of delivery and disappearance of drug to or from the site of action over time include absorption, distribution, metabolism, and elimination. The study of factors that influence how drug concentration varies with time is the subject of pharmacokinetics.
In nearly all cases the site of drug action is located on the other side of a membrane from the site of drug administration. For example, an orally administered drug must be absorbed across a membrane barrier at some point or points along the gastrointestinal (GI) tract. Once the drug is absorbed, and thus passes a membrane barrier of the GI tract, it is transported through the portal vein to the liver and then eventually into systemic circulation (i.e., blood and lymph) for delivery to other body parts and tissues by blood flow. Thus how well a drug crosses membranes is of key importance in assessing the rate and extent of absorption and distribution of the drug throughout different body compartments and tissues. In essence, if an otherwise highly potent drug is administered extravascularly (e.g., oral) but is poorly absorbed (e.g., GI tract), a majority of the drug will be excreted or eliminated and thus cannot be distributed to the site of action.
The principle routes by which drugs disappear from the body are by elimination of unchanged drug or by metabolism of the drug to a pharmacologically active or inactive form(s) (i.e., metabolites). The metabolites in turn may be subject to further elimination or metabolism. Elimination of drugs occurs mainly via renal mechanisms into the urine and to some extent via mixing with bile salts for solubilization followed by excretion through the GI tract, exhaled through the lungs, or secreted through sweat or salivary glands etc. Metabolism for most drugs occurs primarily in the liver.
Each step of drug absorption, distribution, metabolism, and elimination can be described mathematically as a rate process. Most of these biochemical processes involve first order or pseudo-first order rate processes. In other words, the rate of reaction is proportional to drug concentration. For instance, pharmacokinetic data analysis is based on empirical observations after administering a known dose of drug and fitting of the data by either descriptive equations or mathematical (compartmental) models. This permits summarization of the experimental measures (plasma/blood level-time profile) and prediction under many experimental conditions. For example after rapid intravenous administration, drug levels often decline mono-exponentially (first-order elimination) with respect to time as described in Equation 1, where Cp(t) is drug concentration as a function of time, Cp(0) is initial drug concentration, and k is the associated rate constant that represents a combination of all factors that influence the drug decay process (e.g., absorption, distribution, metabolism, elimination).
Cp(t)=Cp(0)etxe2x88x92ktxe2x80x83xe2x80x83(Eq. 1)
This example assumes the body is a single xe2x80x9cwell-mixedxe2x80x9d compartment into which drug is administered and from which it also is eliminated (one-compartment open model). If equilibrium between drug in a central (blood) compartment and a (peripheral) tissue compartment(s) is not rapid, then more complex profiles (multi-exponential) and models (two- and three-compartment) are used. Mathematically, these xe2x80x9cmulti-compartmentxe2x80x9d models are described as the sum of equations, such as the sum of rate processes each calculated according to Equation 1 (i.e., linear pharmacokinetics).
Experimentally, Equation 1 is applied by first collecting time-concentration data from a subject that has been given a particular dose of a drug followed by plotting the data points on a logarithmic graph of time versus drug concentration to generate one type of time-concentration curve. The slope (k) and the y-intercept (C0) of the plotted xe2x80x9cbest-fitxe2x80x9d curve is obtained and subsequently incorporated into Equation 1 (or sum of equations) to describe the drug""s time course for additional subjects and dosing regimes.
When drug concentration throughout the body or a particular location is very high, saturation or nonlinear pharmacokinetics may be applicable. In this situation the capacity of a biochemical and/or physiological process to reduce drug concentration is saturated. Conventional Michaelis-Menten type equations are employed to describe the nonlinear nature of the system, which involve mixtures of zero-order (i.e., saturation:concentration independent) and first-order (i.e., non-saturation:concentration dependent) kinetics. Experimentally, data collection and plotting are similar to that of standard compartment models, with a notable exception being that the data curves are nonlinear. Using a time versus concentration graph to illustrate this point, at very high drug concentration the data line is linear because the drug is being eliminated at a maximal constant rate (i.e., zero-order process). The data line then begins to curve in an asymptotic fashion with time until the drug concentration drops to a point where the rate process becomes proportional to drug concentration (i.e., first-order process). For many drugs, nonlinear pharmacokinetics applies to events such as dissolution of the therapeutic ingredient from a drug formulation, as well as metabolism and elimination. Nonlinear pharmacokinetics also can be applied to toxicological events related to threshold dosing.
Classical one, two and three compartment models used in pharmacokinetics require in vivo blood data to describe time-concentration effects related to the drug decay process, i.e., blood data is relied on to provide values for equation parameters. For instance, while a model may work to describe the decay process for one drug, it is likely to work poorly for others unless blood profile data and associated rate process limitations are generated for each drug in question. Thus, such models are very poor for predicting the in vivo fate of diverse drug sets in the absence of blood data and the like derived from animal and/or human testing.
In contrast to the standard compartment models, physiological-based pharmacokinetic models are designed to integrate basic physiology and anatomy with drug distribution and disposition. Although a compartment approach also is used for physiological models, the compartments correspond to anatomic entities such as the GI tract, liver, lung etc., which are connected by blood flow. Physiological modeling also differs from standard compartment modeling in that a large body of physiological and physicochemical data usually is employed that is not drug-specific. However, as with standard compartment models the conventional physiological models lump rate processes together. Also, conventional physiological models typically fail to incorporate individual kinetic, mechanistic and physiological processes that control drug distribution and disposition in a particular anatomical entity, even though multiple rate processes are represented in vivo. Physiological models that ignore these and other important model parameters contain an underlying bias resulting in poor correlation and predictability across diverse data sets. Such deficiencies inevitably result in unacceptable levels of error when the model is used to describe or predict drug fate in animals or humans. The problem is amplified when the models are employed to extrapolate animal data to humans, and worse, when in vitro data is relied on for prediction in animals or humans.
For instance, the process of drug reaching the systemic circulation for most orally administered drugs can be broken down into two general steps: dissolution and absorption. Since endocytotic processes in the GI tract typically are not of high enough capacity to deliver therapeutic amounts of most drugs, the drugs must be solubilized prior to absorption. The process of dissolution is fairly well understood. However, the absorption process is treated as a xe2x80x9cblack box.xe2x80x9d Indeed, although bioavailability data is widely available for many drugs in multiple animal species and in humans, in vitro and or in vivo data generated from animal, tissue or cell culture permeability experiments cannot allow a direct prediction of drug absorption in humans, although such correlations are commonly used.
B. Computer Systems and Pharmacokinetic Modeling
Computers have been used in pharmacokinetics to bring about easy solutions to complex pharmacokinetic equations and modeling of pharmacokinetic processes. Other computer applications in pharmacokinetics include development of experimental study designs, statistical data treatment, data manipulation, graphical representation of data, projection of drug action, as well as preparation of written reports or documents.
Since pharmacokinetic models are described by systems of differential equations, virtually all computer systems and programming languages that enable development and implementation of mathematical models have been utilized to construct and run them. Graphics-oriented model development computer programs, due to their simplicity and ease of use, are typically used for designing multi-compartment linear and non-linear pharmacokinetic models. In essence, they allow a user to interactively draw compartments and then link and modify them with other iconic elements to develop integrated flow pathways using pre-defined symbols. The user assigns certain parameters and equations relating the parameters to the compartments and flow pathways, and then the model development program generates the differential equations and interpretable code to reflect the integrated system in a computer-readable format. The resulting model, when provided with input values for parameters corresponding to the underlying equations of the model, such as drug dose and the like can then be used to simulate the system under investigation.
While tools to develop and implement pharmacokinetic models exist and the scientific literature is replete with examples, pharmacokinetic models and computer systems developed to date have not permitted sufficient predictability of the pharmacokinetic fate of extravascularly administered drugs in a mammal from in vitro cell, tissue or compound structure-activity relationship (SAR/QSAR) data. A similar problem exists when attempting to predict absorption of a compound in one mammal (e.g., human) from data derived from a second mammal (e.g., dog). For example, existing pharmacokinetic models of oral absorption use several different approaches to predict oral absorption and fraction dose absorbed (Amidon et al., Pharm. Res., (1988) 5:651-654; Chiou, W. L., Int. J Clin. Pharmacol. Ther., (1994) 32:474-482; Chiou, W. L., Biopharm. Drug Dispos., (1995) 16:71-75; Dressman et al., J. Pharm. Sci., (1985) 74:588-589; Lennernas et al., J. Pharm. Pharmacol., (1997) 49:682-686; Levet-Trafit et al., Life Sciences., (1996) 58:PL359-63; Sinko et al., Pharm. Res., (1991) 8:979-988; and Soria et al.,. Biopharm. Drug Dispos., (1996) 17:817-818). Unfortunately, these models are flawed as they make mathematical assumptions that limit prediction to particular compounds, and the correlation function is sigmoidal in shape (i.e., high/steep slope). Therefore the predictive power of such models for compounds outside a relatively small group is very limited. This is particularly true for collections of compounds possessing variable ranges of dosing requirements and of permeability, solubility, dissolution rates and transport mechanism properties. Other drawbacks include use of drug-specific parameters and values in pharmacokinetic models from the outset of model development, which essentially limits the models to drug-specific predictions. These and other deficiencies also impair generation of rules that universally apply to drug disposition in a complex physiological system such as the GI tract.
Extravascular administration of drugs is the preferred route for physicians, patients, and drug developers alike due to lower product price, increased patient compliance, ease of administration. Current assessment of the bioavailability of extravascularly administered drugs and lead drug compounds, as well as bioavailability of intravascularly administered compounds relative to specialized barriers to absorption such as the blood brain barrier, is limited in large part to animal and human testing. The economic and medical consequences of problems with drug absorption and variable bioavailability are immense. Failing to identify promising or potentially problematic drug candidates during the discovery and pre-clinical stages of drug development is one of the most significant consequences of problems with drug bioavailability. Accordingly, there is a need to develop a comprehensive, physiologically-based pharmacokinetic model and computer system capable of predicting drug bioavailability and variability in humans that utilizes relatively straightforward input parameters. Furthermore, considering the urgent need to provide the medical community with new therapeutic alternatives and the current use of high throughput drug screening for selecting lead drug candidates, a comprehensive biopharmaceutical computer-based tool that employs a modeling approach for predicting bioavailability of compounds and compound formulations is needed.
Various publications review gastrointestinal anatomy and physiology including motility, secretion, absorption, and digestion, as well as gastrointestinal pharmacology and physiology in gastrointestinal diseased individuals (See, e.g., L. Johnson ed., Physiology of the Gastrointestinal Tract, Second edition, Vol. 2, Ravind Press (1987); Kutchai, Gastrointestinal System, Part IV, Principles of Physiology, Mosby Press (1996); and Sleisenger, Gastrointestinal Disease, 3rd edition, Saunders (1983)). Sharget et al. (Physiological Factors Related to Drug Absorption, Applied Biopharmaceutics and Pharmacokinetics (1993)) review pharmacokinetics and compartment modeling. Various pharmacokinetic models of oral drug absorption are disclosed in Grass, G. (Advanced Drug Delivery Reviews (1997) 23:199-219); Amidon et al., (Pharm. Res. (1988) 5:651-654); Chiou. W. L., (Int. J. Clin. Pharmacol. Ther., (1994) 32:474-482); Chiou, W. L., (Biopharm. Drug Dispos., (1995) 16:71-75); Dressman et al., (J. Pharm. Sci., (1985) 74:588-589); Lennernas et al., (J. Pharm. Pharmacol., (1997) 49:682-686); Levet-Trafit et al., (Life Sciences., (1996) 58:PL359-63); Sinko et al., (Pharm. Res., (1991) 8:979-988); and Soria et al.,. (Biopharm. Drug Dispos., (1996) 17:817-818)).
The present invention relates to a pharmacokinetic-based design and selection tool (PK tool) and methods for predicting absorption of a compound in a mammalian system of interest. The methods utilize the tool, and optionally a separately operable component or subsystem thereof.
The PK tool comprises as computer-readable components: (1) input/output system; (2) physiologic-based simulation model of one or more segments of a mammalian system of interest having one or more physiological barriers to absorption that is based on the selected route of administration; and (3) simulation engine having a differential equation solver, and optionally, a control statement module. The physiologic-based simulation model of the PK tool of the invention is a multi-compartment mathematical model comprising as operably linked components: (i) differential equations for one or more of fluid transit, fluid absorption, mass transit, mass dissolution, mass solubility, and mass absorption for one or more segments of the mammalian system of interest; and (ii) initial parameter values for the differential equations corresponding to physiological parameters and selectively optimized adjustment parameters, and optionally regional correlation parameters, for one or more segments of the mammalian system of interest; and, optionally, (iii) control statement rules for one or more of transit, absorption, permeability, solubility, dissolution, concentration, and mathematical error correction for one or more segments of the mammalian system of interest.
The computer-readable input/output system, physiologic-based simulation model, and simulation engine of the PK tool are capable of working together to carrying out the steps of: (1) receiving through the input/output system data comprising dose, permeability and solubility data of a compound of interest for one or more segments of the mammalian system of interest; and (2) applying the physiologic-based simulation model and simulation engine to generate an absorption profile for the compound characterized by one or more of concentration, rate of absorption, and extent of absorption relative to a selected sampling site that is across a physiological barrier for one or more segments of the mammalian system of interest.
The present invention also provides a database for utilization in the PK tool and method of the invention. The database includes one or more physiologic-based simulation models of the invention. Additional databases are provided for simulation model parameters, and may be integrated or separate from a database having a simulation model of the invention. The database(s) includes one or more of (i) differential equations for one or more of fluid transit, fluid absorption, mass transit, mass dissolution, mass solubility, and mass absorption for one or more segments of the mammalian system of interest; (ii) initial parameter values for the differential equations corresponding to physiological parameters and selectively optimized adjustment parameters, and optionally regional correlation parameters, for one or more segments of the mammalian system of interest; and (iii) control statement rules for one or more of transit, absorption, permeability, solubility, dissolution, concentration, and mathematical error correction for one or more segments of the mammalian system of interest. The database(s) have a compartment-flow data structure that is portable into and readable by a simulation engine for calculating time-dependent rate of absorption, extent of absorption, and concentration of a compound at a sampling site across a physiological barrier of one or more segments of the mammalian system of interest.
The invention also includes a method for selectively optimizing a pharmacokinetic-based simulation model for use in the PK tool of the invention. This method permits the PK tool of the invention to accurately predict one or more in vivo pharmacokinetic properties of a compound in a mammalian system of interest from input data derived from a selected in vitro or in vivo data source. The method includes the steps of (i) generating initial adjustment parameter values for one or more independent parameters of the simulation model by utilizing a curve-fitting algorithm to simultaneously fit to the model one or more input variables corresponding to a pharmacokinetic property of a compound test set derived from (a) a first data source corresponding to the mammalian system of interest, and (b) a second data source corresponding to a system other than the mammalian system of interest; (ii) selecting adjustment parameter values that permit correlation of one or more of the input variables from the first data source to one or more input variables from the second data source; (iii) repeating steps (i) and (ii) one or more times for one or more additional independent parameters of the simulation model until deviation of the correlation is minimized; and (iv) utilizing the selected adjustment parameters as constants for the independent parameters in the simulation model.
The present invention further includes a method for producing a pharmacokinetic-based simulation model for use in the PK tool that facilitates estimation of a selected parameter value in a first segment of mammalian system of interest utilizing input data for the selected parameter that corresponds to a second segment of the mammalian system of interest. The method involves (i) providing a logic function module in the simulation model that includes a set of regional correlation parameter values for at least first and second segments of the mammalian system of interest that facilitates estimation of a selected parameter value in the first segment of the mammalian system of interest utilizing input data for the selected parameter that corresponds to the second segment of the mammalian system of interest; and (ii) providing a control statement in the simulation model which initiates the regional correlation estimation function of the logic function module when a value for the first segment is not supplied as input into the model.
The present invention also provides a method for generating formulation profiles for a compound of interest utilizing the PK tool of the invention.
The PK tool of the invention may be provided as a computer system, as an article of manufacture in the form of a computer-readable medium, or a computer program product and the like. Subsystems and individual components of the PK tool also can be utilized and adapted in a variety of disparate applications for predicting the fate of an administered compound. The PK tool and methods of the invention can be used to screen and design compound libraries, select and design drugs, as well as predict drug efficacy in mammals from in vitro and/or in vivo data of one or more compounds of interest. The PK tool and methods of the invention also finds use in selecting, designing, and preparing drug compounds, and multi-compound drugs and drug formulations (i.e., drug delivery system) for preparation of medicaments for use in treating mammalian disorders.
Absorption: Transfer of a compound across a physiological barrier as a function of time and initial concentration. Amount or concentration of the compound on the external and/or internal side of the barrier is a function of transfer rate and extent, and may range from zero to unity.
Bioavailability: Fraction of an administered dose of a compound that reaches the sampling site and/or site of action. May range from zero to unity. Can be assessed as a function of time.
Compound: Chemical entity.
Computer Readable Medium: Medium for storing, retrieving and/or manipulating information using a computer. Includes optical, digital, magnetic mediums and the like; examples include portable computer diskette, CD-ROMs, hard drive on computer etc. Includes remote access mediums; examples include internet or intranet systems. Permits temporary or permanent data storage, access and manipulation.
Data: Experimentally collected and/or predicted variables. May include dependent and independent variables.
Dissolution: Process by which a compound becomes dissolved in a solvent.
Input/Output System: Provides a user interface between the user and a computer system.
Permeability: Ability of a physiological barrier to permit passage of a substance. Refers to the concentration-dependent or concentration-independent rate of transport (flux), and collectively reflects the effects of characteristics such as molecular size, charge, partition coefficient and stability of a compound on transport. Permeability is substance and barrier specific.
Physiologic Pharmacokinetic Model: Mathematical model describing movement and disposition of a compound in the body or an anatomical part of the body based on pharmacokinetics and physiology.
Production Rule: Combines known facts to produce (xe2x80x9cinferxe2x80x9d) new facts. Includes production rules of the xe2x80x9cIF . . . THENxe2x80x9d type.
Simulation Engine: Computer-implemented instrument that simulates behavior of a system using an approximate mathematical model of the system. Combines mathematical model with user input variables to simulate or predict how the system behaves. May include system control components such as control statements (e.g., logic components and discrete objects).
Solubility: Property of being soluble; relative capability of being dissolved.
Transport Mechanism: The mechanism by which a compound passes a physiological barrier of tissue or cells. Includes four basic categories of transport: passive paracellular, passive transcellular, carrier-mediated influx, and carrier-mediated efflux.